Explanation Approach: The expected value of X , denoted by E ( X ) is given by, E ( X ) = x 1 p 1 + x 2 p 2 + ........ + x n p n Here, x 1 , x 2 , ........ , x n are the values of random variable X with associated probabilities p 1 , p 2 , ....... , p n respectively. Calculation: Let X denote the number of boys in a four child family. The random variable X can take the values, X = { 0 , 1 , 2 , 3 , 4 } The sample space for the event is, S = { ( B , B , B , B ) , ( B , B , B , G ) , ( B , B , G , G ) , ( B , G , G , G ) , ( G , G , G , G ) } The probabilities for different values of X are, P ( X = 0 ) = 1 5 P ( X = 1 ) = 1 5 P ( X = 2 ) = 1 5 P ( X = 3 ) = 1 5 And, P ( X = 4 ) = 1 5 Thus, the expected value of the random variable X is,

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Author: Tan

Publisher: CENGAGE C

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Chapter 8.2, Problem 4E

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Solution Summary: The author explains how the expected number of boys in a four child family is 2.

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